Time-dependent Sobolev inequality along the Ricci flow
Chengjie Yu
TL;DR
This paper establishes a time-dependent Sobolev inequality along the Ricci flow, extending previous results, and applies it to analyze the growth of the ratio of bob-collapsing in the flow.
Contribution
It introduces a generalized time-dependent Sobolev inequality along the Ricci flow, building upon and extending earlier work by Zhang, Ye, and Hsu.
Findings
Derived a new time-dependent Sobolev inequality for Ricci flow
Applied the inequality to analyze bob-collapsing growth
Provided insights into geometric behavior under Ricci flow
Abstract
In this article we get a time-dependent Sobolev inequality along the Ricci flow which generalizes the earlier results of Zhang, Ye, Hsu. As an application of the time-dependent Sobolev inequality, we also get a growth of the ratio of bob-collapsing along the Ricci flow.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Analytic and geometric function theory